Canonical Reduction of the Self-Dual Yang Mills Equations to Complex Ginzburg-Landau Equations and Exact Solutions

Authors

  • Abdel Rahman M. Shehata minia university
  • Jammel F. Al-Zaidy taif university

Keywords:

SDYM, complex Ginzburg-Landau, B̈cklund transformations

Abstract

The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills
(SDYM) theory to two-dimensional complex Ginzburg-Landau equation are considered.  On the other hand, other methods and transformations are developed to obtain exact solu-tions for the original two dimensional complex Ginzburg-Landau equation. The corres-ponding gauge potential  and the gauge field strengths are also obtained. For these nonlinear evolution equations (NLEEs) which describe pseudo-spherical surfaces (pss) two new exact solution classes are generated from known solutions by us-ing the B̈cklund transformations with the aid of Mathematica,either the seed solution is constant or a traveling wave.

Author Biographies

  • Abdel Rahman M. Shehata, minia university
    math. dept. ph.d
  • Jammel F. Al-Zaidy, taif university
    math.dept. M.Sc.

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Published

2017-04-20

Issue

Vol. 10 No. 3: (April 2017)

Section

Mathematical Physics

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How to Cite

Canonical Reduction of the Self-Dual Yang Mills Equations to Complex Ginzburg-Landau Equations and Exact Solutions. (2017). European Journal of Pure and Applied Mathematics, 10(3), 563-573. https://www.ejpam.com/index.php/ejpam/article/view/2219